1x 2y 15.95 3x 5y 45.90 Algebra Calculator

This calculator solves the system of linear equations: 1x + 2y = 15.95 and 3x + 5y = 45.90. It provides the values of x and y that satisfy both equations simultaneously.

How to Use This Calculator

To solve the system of equations:

Enter the coefficients for x and y in the first equation (1x + 2y = 15.95)
Enter the coefficients for x and y in the second equation (3x + 5y = 45.90)
Click "Calculate" to find the solution
Review the results and interpretation

Note: This calculator assumes the system has exactly one solution. If the equations are dependent or inconsistent, the calculator will indicate this.

Formula Explained

For a system of equations:

a₁x + b₁y = c₁

a₂x + b₂y = c₂

The solution can be found using the following formulas:

x = (b₂c₁ - b₁c₂) / (a₁b₂ - a₂b₁)

y = (a₁c₂ - a₂c₁) / (a₁b₂ - a₂b₁)

For our specific equations:

1x + 2y = 15.95

3x + 5y = 45.90

The determinant (a₁b₂ - a₂b₁) is calculated as (1×5 - 3×2) = (5 - 6) = -1.

Worked Example

Let's solve the system:

1x + 2y = 15.95

3x + 5y = 45.90

Calculate the determinant: (1×5 - 3×2) = -1
Calculate x: (5×15.95 - 2×45.90) / -1 = (79.75 - 91.80) / -1 = (-12.05) / -1 = 12.05
Calculate y: (1×45.90 - 3×15.95) / -1 = (45.90 - 47.85) / -1 = (-1.95) / -1 = 1.95

The solution is x = 12.05 and y = 1.95.

Interpreting Results

The calculator provides two values:

x value: The solution for x that satisfies both equations
y value: The solution for y that satisfies both equations

If the determinant is zero, the system either has infinitely many solutions (dependent equations) or no solution (inconsistent equations).

Tip: Always verify your results by plugging the values back into the original equations.

Frequently Asked Questions

What if the determinant is zero?: The system either has infinitely many solutions (dependent equations) or no solution (inconsistent equations).
Can this calculator solve systems with more than two variables?: No, this calculator is designed specifically for two-variable systems.
How accurate are the results?: The calculator uses standard algebraic methods and provides precise decimal solutions.
What if I enter non-linear equations?: This calculator is designed for linear equations only. Non-linear systems require different methods.
Can I use this calculator for real-world problems?: Yes, the solutions can be applied to any real-world scenario involving two variables and two linear equations.